NAG Library Function Document

nag_zwaxpby (f16ghc)

 Contents

    1  Purpose
    7  Accuracy

1
Purpose

nag_zwaxpby (f16ghc) computes the sum of two scaled vectors, preserving input, for complex scalars and vectors.

2
Specification

#include <nag.h>
#include <nagf16.h>
void  nag_zwaxpby (Integer n, Complex alpha, const Complex x[], Integer incx, Complex beta, const Complex y[], Integer incy, Complex w[], Integer incw, NagError *fail)

3
Description

nag_zwaxpby (f16ghc) performs the operation
w αx+βy,  
where x and y are n-element complex vectors, and α and β are complex scalars.

4
References

Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001) Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard University of Tennessee, Knoxville, Tennessee http://www.netlib.org/blas/blast-forum/blas-report.pdf

5
Arguments

1:     n IntegerInput
On entry: n, the number of elements in x, y and w.
Constraint: n0.
2:     alpha ComplexInput
On entry: the scalar α.
3:     x[dim] const ComplexInput
Note: the dimension, dim, of the array x must be at least max1,1+n-1×incx.
On entry: the n-element vector x.
If incx>0, xi must be stored in x[i-1×incx], for i=1,2,,n.
If incx<0, xi must be stored in x[n-i×incx], for i=1,2,,n.
Intermediate elements of x are not referenced. If n=0, x is not referenced and may be NULL.
4:     incx IntegerInput
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
5:     beta ComplexInput
On entry: the scalar β.
6:     y[dim] const ComplexInput
Note: the dimension, dim, of the array y must be at least max1,1+n-1×incy.
On entry: the n-element vector y.
If incy>0, yi must be stored in y[i-1×incy], for i=1,2,,n.
If incy<0, yi must be stored in y[n-i×incy], for i=1,2,,n.
Intermediate elements of y are not referenced. If β=0.0 or n=0, y is not referenced and may be NULL.
7:     incy IntegerInput
On entry: the increment in the subscripts of y between successive elements of y.
Constraint: incy0.
8:     w[dim] ComplexInput/Output
Note: the dimension, dim, of the array w must be at least max1,1+n-1×incw.
On entry: if incw1, intermediate elements of w may contain values and will not be referenced; the other elements will be overwritten and need not be set.
On exit: the elements wi of the vector w will be stored in w as follows.
If incw>0, wi is in w[i-1×incw], for i=1,2,,n.
If incw<0, wi is in w[n-i×incw], for i=1,2,,n.
Intermediate elements of w are not referenced.
9:     incw IntegerInput
On entry: the increment in the subscripts of w between successive elements of w.
Constraint: incw0.
10:   fail NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6
Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, incw=value.
Constraint: incw0.
On entry, incx=value.
Constraint: incx0.
On entry, incy=value.
Constraint: incy0.
On entry, n=value.
Constraint: n0.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

7
Accuracy

The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001)).

8
Parallelism and Performance

nag_zwaxpby (f16ghc) is not threaded in any implementation.

9
Further Comments

None.

10
Example

This example computes the result of a scaled vector accumulation for
α=3+2i,   x = -6+1.2i,3.7+4.5i,-4+2.1iT , β=-i,   y = -5.1,6.4-5i,-3-2.4iT .  
x and y, and also the sum vector w, are stored in reverse order.

10.1
Program Text

Program Text (f16ghce.c)

10.2
Program Data

Program Data (f16ghce.d)

10.3
Program Results

Program Results (f16ghce.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017